Show that a simple graph with $6$ vertices, $11$ edges, and more than one component cannot exist.
I don't understand why can't there be a simple graph with those edges and vertices. By definition of graph we have $|\text{Edges}| \geq |\text{Vertices}|-|\text{components}|$
So from this definition it's correct: $11 \geq 6-w$
Best Answer
If a component has only one vertex it has no edges, and the remaining five vertices can have at most 10 edges.
If a component has two vertices it gets worse since that component has only one edge, and the remaining 4 vertices have at most 6 edges. Other cases just as bad.